Modeling and Analysis of Swarms

Kevin Passino
Electrical and Computer Engineering, The Ohio State University

(April 1, 2010 11:30 AM - 12:18 PM)

Modeling and Analysis of Swarms

Abstract

In a honey bee swarm, the actions of thousands of worker bees dynamically combine in several social decision-making processes that serve the colony as a whole. During "social foraging", the colony optimally allocates foragers according to the relative profitability of forage sites. A homeless swarm performs "nest-site selection" by having a small subset of the bees quickly search for, and agree on, the best new home it can find. After agreement, all the bees in the swarm take flight to migrate to their new home. Flight guidance occurs via "leader" bees streaking fast through the swarm in the direction of the new nest site and "followers" orienting their flight in the direction of the leaders and chasing them. In the first part of the talk, these three honeybee distributed decision making processes are overviewed and progress on their modeling and analysis is summarized. The second part of the talk focuses in more detail on midge swarms. Individual midge motion dynamics, sensing abilities, and flight rules are represented with a dynamical model. The sensing accuracy and flight rule are adjusted so that the model produces trajectory behavior, and velocity, speed, and acceleration distributions, that are remarkably similar to those found in midge swarm experiments. Mathematical cohesiveness analysis of the validated swarm model shows that the distances between the midges' positions and the swarm position centroid, and the midges' velocities and the swarm velocity centroid, are ultimately bounded (i.e., eventually satisfy a bound expressed in terms of individual midge parameters). Likewise, the swarm position and velocity centroids are shown to be ultimately bounded. Apparently, this is the first time that a validated swarm model has yielded itself to analytical studies.